![](bg2.png)
– Shi-Xin, et al. [4], propose an access control model to achieve a fine-grained, data
confidentiality and scalability via a formal definition of the HABAC model (Hier-
archy Attribute-Based Access Control).
– Adamov and Hahanov [5], define a security model for individual cyberspace (ICS)
protection as a means to ensure a secured user’s virtual environment, they establish
an analysis of security issues related to ICS and propose a conceptual model for
modern security environments.
– Freitas and Paul [6], present an abstract formalisation of federated cloud workflows
using the Z notation. They define various properties using rules restricting valid
options in two categories: security and cost.
– Binz, et al. [7], propose Enterprise Topology Graphs (ETG) as formal model to
describe an enterprise topology. Based on the established graph theory, ETG bring
formalization and provability to the cloud. Also, authors show how ETG can im-
prove the environmental impact of the enterprise IT.
Consequently, cloud computing paradigm lacks a formal and verifiable model of its
basic concepts: service delivery and deployment models, only some technological at-
tempts are realized; for virtualization as it has been done in [2] and [3], for security as
in [4], [5] and [6], or for enterprise IT as in [7].
In this work, we adopt, Bigraphical Reactive Systems (BRS), proposed by Milner
[8] , as a formalism to specify fundamental aspects of cloud computing. In particular,
we propose a theoretical framework based on BRS aiming to formalize relationships
between service providers and customers in different delivery and deployment models
of cloud computing. Based on a judicious coupling between bigraphs theory as a se-
mantic framework and Maude language[9] as a specification language, we propose the
Bigraphical Maude-Based Model Checker (BMMC) that combines logical reflection
and hierarchical structuring of the underlying adopted theoretical framework to simply
execute and verify complex cloud systems. The proposed approach is validated through
a concrete verification of two cloud computing inherent properties: service availability
and quick scalability.
This paper is arranged as follows. In the next section we define the bigraphical model
for cloud computing. Section 3 presents a mapping of the defined model to Maude-
based specification and exploits it to formally verify cloud systems. Finally, conclusion
and future work are addressed in section 4.
2 BRS for Cloud Computing Specification
A BRS (Bigraphical Reactive Systems) [8] consists of a category of bigraphs and a
set of reaction rules that may be applied to transform these bigraphs. The bigraph as
an ordinary graph is composed of nodes and edges, unlike nodes in a bigraph can be
nested giving rise to hierarchical and larger bigraphs. Additionally, it is the resulting
graph of composing a link graph; representing interconnection between nodes, and a
place graph; expressing the physical locations of theses nodes; hence the prefix ”bi” in
bigraph.
4